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ECM33 2022

Marcin Stachowicz1, Agnieszka Huć1, Anna Hoser2 and Krzysztof Woźniak2

marcin.stachowicz@.uw.edu.pl 

 

1Department of Geochemistry, Mineralogy and Petrology,

University of Warsaw, Żwirki i Wigury 93, Warszawa, 02-089, Poland

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2Department of Chemistry Biological and Chemical Research Centre, University of Warsaw, Żwirki i Wigury 101, Warszawa 02-093, Poland

X-ray diffraction and periodic DFT calculations for modelling of hydrogen atoms in a mineral - pinnoite

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The crystal structure

Pinnoite MgB2O(OH)6

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Applied formalism and experimental details

Independent Atom Model, shelxl refinement

Normal Mode Refinement NOMORE online package

https://nomore.chem.uw.edu.pl/

Multipole model, QTAIM, In-house X-ray diffractometer, Diamond Anvil Cell

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Pressure effects on Mg, B, O and H

Scope of the presentation

Modelling of hydrogen atoms in a mineral pinnoite

What is the effect of pressure on individual atoms/ions in the crystal structure of pinnoite?

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The crystal structure pinnoite MgB2O(OH)6

View along [110]

View along [001]

View along [100]

5x5x5 super cell

The specimen

P42/n

a=7.61750(4) Å

c = 8.19338(9) Å

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Diacell© One20DAC

-Very wide angle DAC for X-ray Applications 

~100o access window

-Fitted with 4mm Boehler-Almax anvils mounted on conical WC seats

Diamond Anvil Cell,

Type Ia, Boehler Almax 4.00-120°

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NoMoRe workflow

NoMoRe – Normal Mode Refinement

Hoser A. A., Madsen A. Ø.

Acta Cryst. (2016). A72, 206

https://nomore.chem.uw.edu.pl/

Crystal17, periodic calculations

DFT

B3LYP functional

6-31G** basis sets

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ADPs elongated along c in 1.5GPa experiment in the IAM model

U3/U1

-----

2.00

1.88

1.39

2.46

1.79

1.93

Mg1

O1

O2

O3

O4

B1

IAM

U1, U2, U3 are the three Main Axes Components of Uij

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Improvement after NOMORE for 1.5 GPa HP experiment in DAC

U1, U2, U3 are the three Main Axes Components of Uij

U3/U1

-----

2.00

1.88

1.39

2.46

1.79

1.93

Mg1

O1

O2

O3

O4

B1

1.71

1.73

1.62

2.09

1.76

1.73

Mg1

O1

O2

O3

O4

B1

IAM

NOMORE

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Comparison of displacement parameters U

U1, U2, U3 are the three Main Axes Components of Uij

Equivalent Isotropic Displacement Parameters

U1, U2, U3 are the three Main Axes Components of Uij

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Comparison of displacement parameters U

U1, U2, U3 are the three Main Axes Components of Uij

Equivalent Isotropic Displacement Parameters

U1, U2, U3 are the three Main Axes Components of Uij

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Multipole model

NOMORE

IAM ambient

Multipol model

ambient

NOMORE

ambient

NOMORE

4 GPa

NOMORE

1.5 GPa

IAM

1.5 GPa

IAM

4 GPa

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Spherical harmonics

P42/n

 

MgB2O(OH)6 crystal symmetry

local

symmetry

 

Multip.

Wyckoff

letter

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  • Aspherical atom model

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  • Topological Analysis (QTAIMC)

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    • Atomic basins

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Hansen, N. K. & Coppens, P. Acta Crystallographica Section A, 34, 909–921 (1978).

Volkov, A., Macchi, P., Farrugia, L. J., Gatti, C.,Mallinson, P., Richter, T. & Koritzansky, T. XD2016. University at Buffalo, State University of New York, NY, USA; University of Milan, Italy; University of Glasgow, UK; CNRISTM, Milan, Italy; Middle Tennessee State University, TN, USA; and Freie Universitat, Berlin, Germany, (2016).

Bader R. F. W. Atoms in Molecules – A Quantum Theory, Oxford University Press, Oxford (1990).

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Atomic basin representation of atoms

Mg atomic basin vs MgO6 coordination octahedron

B atomic basin vs BO4 coordination tetrahedron

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Mg(1) Tracing electron density redistribution with HP

Overlay of atomic basins at ambient pressure and under 1.5 GPa (green)

Electron density contracted around boning regions

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Relaxation in non-bonding directions

ambient

1.5 GPa

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O(1) O(2) O(3) Tracing electron density redistribution with HP

ambient

1.5 GPa

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O(1)

overlay

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ambient

1.5 GPa

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overlay

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O(2)

overlay

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ambient

1.5 GPa

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  • Contraction around bond to B

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  • Expansion towards bond to Mg

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  • Expansion in non-bonding areas

O(3)

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H(1) H(2) H(3) Tracing electron density redistribution with HP

ambient

1.5 GPa

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H(1)

overlay

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ambient

1.5 GPa

​

overlay

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H(2)

overlay

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1.5 GPa

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  • Contraction around bond to B

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  • Expansion towards bond to Mg

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  • Expansion in non-bonding areas

H(3)

overlay

2nd view

overlay

2nd view

overlay

2nd view

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B(1) Tracing electron density redistribution with HP

Overlay of atomic basins at ambient pressure and under 1.5 GPa (green)

negative compressibility due to charge redistribution

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Atomic basin volume increased by 36% with pressure

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ambient

1.5 GPa

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O(4) Tracing electron density redistribution with HP

Overlay of atomic basins at ambient pressure and under 1.5 GPa (green)

Electron density contracted around boning regions

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Relaxation on edges

ambient

1.5 GPa

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Integrated properties of Bader atomic basins

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Q[e]

Vtot [Å3]

Mg

1.57

5.7

O(4)

-1.45

11.1

O(2)

-1.24

13.1

O(1)

-1.33

14.2

O(3)

-1.35

15.3

B

2.45

1.1

H(2)

0.44

2.3

H(1)

0.53

2.3

H(3)

0.48

2.7

1.5GPa

Q[e]

Vtot [Å3]

Mg

1.53

5.9

O(4)

-0.78

10.0

O(2)

-1.44

13.37

O(1)

-1.56

14.4

O(3)

-1.44

15.2

B

2.28

1.5

H(2)

0.61

1.6

H(1)

0.61

2.0

H(3)

0.57

2.4

Charge per formula unit +0.08e +0.01e

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Summary

  • NOMORE package allowed for determination of ADPs of H in pinnoite

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    • Corrections of ADPs in all atoms in high pressure DAC experiment

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  • Atoms compress anisotropically
    • Charge redistribution can lead to negative compressibility of atomic basin (B)

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    • Expansion of electron density in non-bonding directions

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    • Contraction of electron density around bonding directions (Mg towards O, O towards B)

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Thank you for listening

Acknowledgements

Anna Hoser

Agnieszka Huć

Krzysztof Woźniak

Funding

Polish National Science Centre (NCN) OPUS17 grant - decision DEC-2019/33/ B/ST10/02671

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This research was supported in part by PLGrid Infrastructure with computing power

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Crystal orientation for maximum completeness in a DAC high pressure experiment

www.DTools.pl

ECM33 Poster: MS27-2-4

Code developed by Daniel Tchoń

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Tchoń. D. and Makal A. Maximizing completeness in single-crystal high-pressure diffraction experiments: phase transitions in 2°AP IUCrJ 8, 6, 1006–1017 (2021)

Diacell© One20DAC

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The first attempt to study the atomic structure of pinnoite was published in 1946 by Stadler[1]. He determined the unit cell parameters and suggested the P42/n space group. In 1957 Paton and MacDonald[2] collected new data and solved the structure in the P42/n group but recognized this solution as a pseudosymmetrical variant of the P42 space group. The refinement converged with R(F)=22%. In 1967 Krough-Moe[3] used the data from the previous study by Paton and MacDonald and refined the structure in the P42 space group with R(F)=15,7%. The R(F) improvement was an argument that the P42 space group is more accurate. Krough-Moe pointed out that the value of the B-O-B angle obtained in the higher symmetry solution was too small; 111,6o.

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In the P42 space group, there are two symmetrically independent B atoms B2O[OH]6 groups, and the B-O-B angles obtained by Krough-Moe were 120o and 127o.

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In 1983 Genkina and Malinovskii[4] collected new data for this system and refined it with the P42 space group with R(F)= 3,3%. The values of B-O-B angles were 115o and 125o in this case.

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1. Stadler, H. P. (1947). The cell dimensions and space-group of pinnoite. Mineralogical magazine and journal of the Mineralogical Society, 28(196), 26-28.

2. Paton F, MacDonald S G G (1957) The crystal structure of pinnoite Acta Crystallographica 10 653-656

3. Krogh-Moe J (1967) A note on the structure of pinnoite Acta Crystallographica 23 500-501.

4. Genkina E A, Malinovskii Y A (1983) Refinement of the structure of pinnoite: Location of hydrogen atoms Soviet Physics Crystallography 28 475-477

Pinnoite crystal structure

studies

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In this study data up to the high resolution of 0.4 Å were collected.

I/σ ratio of the reflections forbidden in the P42/n space group:

I/σ = 0.1 for the absences associated with the n plane and

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I/σ = 0.3 for for the absences associated the absences 42 axis.

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The mean I/σ ratio for all reflections in the dataset was 8.3.

SAMPLE

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Formula

Mg[B2O(OH)6]

Space group

P42/n

a=b [Å]

7.6174

c [Å]

8.1946

Unit cell volume [Å3]

479.5

Z

4

DATA COLLECTION

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Crystal dimensions [mm]

0.15x0.15x0.15

Radiation

MoKα

Temperature K}

293

Resolution [Å]

0.4

Completness

100%

Reflections collected

42967

Average redundancy (P42)

18

Rint

0.044

hk0 plane; odd reflections are abesnt

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In this study data up to the high resolution of 0.4 Å were collected.

I/σ ratio of the reflections forbidden in the P42/n space group:

I/σ = 0.1 for the absences associated with the n plane and

​

I/σ = 0.3 for for the absences associated the absences 42 axis.

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The mean I/σ ratio for all reflections in the dataset was 8.3.

IAM refinement in both space groups

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P42/n P42

R1=2.02% R1=2.29%

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B-O-B angle 119o 120o and 119o

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P42/n

IAM 1.5GPa

Multipole model 1.5 GPa

NOMORE 1.5 GPa

IAM 4.2 GPa

NOMORE 4.2 GPa

IAM ambient P

Multipole model

NOMORE

a/Å

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7.5686(4)

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7.4824(9)

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7.61750(4)

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b/Å

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7.5686(4)

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7.4824(9)

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7.61750(4)

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c/Å

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8.156(5)

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8.0584(7)

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8.19338(9)

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Volume/Å3

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467.2(3)

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451.16(11)

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475.432(8)

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ρcalcg/cm3

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2.331

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2.414

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2.291

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μ/mm‑1

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0.351

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0.363

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0.344

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F(000)

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336.0

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336.0

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336.0

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Radiation

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MoKα (λ = 0.71073)

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MoKα (λ = 0.71073)

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MoKα (λ = 0.71073)

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2Θ range for data collection/°

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7.344 to 73.096

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7.432 to 68.228

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7.304 to 131.846

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Index ranges

-12 ≤ h ≤ 11, -12 ≤ k ≤ 12, -4 ≤ l ≤ 4

-10 ≤ h ≤ 10, -6 ≤ k ≤ 6, -12 ≤ l ≤ 12

-19 ≤ h ≤ 19, -19 ≤ k ≤ 19, -17 ≤ l ≤ 20

Reflections collected

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4526

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3893

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73942

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Independent reflections

501 [Rint = 0.0551, Rsigma = 0.0272]

379 [Rint = 0.0667, Rsigma = 0.0387]

4224 [Rint = 0.0452, Rsigma = 0.0138]

Data/restraints/parameters

501/3/60

501/0/101

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379/3/60

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4224/3/60

4224/0/214

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Goodness-of-fit on F2

1.101

1.579

1.222

1.039

1.084

1.098

0.997

1.375

Final R indexes [I>=2σ (I)]

R1 = 0.0435, wR2 = 0.1067

R1 = 0.035

R1 = 0.0466, wR2 = 0.1268

R1 = 0.0451, wR2 = 0.1074

R1 = 0.0494, wR2 = 0.1248

R1 = 0.0202, wR2 = 0.0551

R1 = 0.015

R1 = 0.0254, wR2 = 0.0705

Final R indexes [all data]

R1 = 0.0488, wR2 = 0.1102

R1 = 0.043, wR2 = 0.09

R1 = 0.0520, wR2 = 0.1299

R1 = 0.0683, wR2 = 0.1211

R1 = 0.0724, wR2 = 0.1377

R1 = 0.0245, wR2 = 0.0575

R1 = 0.022, wR2 = 0.037

R1 = 0.0297, wR2 = 0.0725

Largest diff. peak/hole / e Å-3

0.38/-0.70

0.33/-0.45

0.38/-0.79

0.34/-0.33

0.30/-0.34

0.39/-0.27

0.17/-0.19

0.51/-0.54

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View along b*

View along c*

HP experiment

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Suboptimal crystal orientation + limited access to the reciprocal space

influences the shape of ADPs

SE image of pinnoite